The following method for downloading an older version of an app works fine with iTunes 12.6.2 and earlier. Alas iTunes 12.7 and later no longer support app downloads, and as of 14 September 2017 it's not yet clear whether Apple will provide some other way for users to download the last compatible version of an app or not.

If your iOS device is running iOS 7 or older, you must use an older version of each Geometry Games app. It's easy to download an older version, but the procedure is not at all obvious. You must:

Open iTunes on your Mac or PC and download the desired app, using the same Apple ID that you use on your iOS device. Don't try to install the app from iTunes directly onto your device – at this point you've downloaded the current version of the app, which requires iOS 8 or later and won't work on your older device.

Quit iTunes on your Mac or PC, then launch the App Store app directly on your iOS device, using that same Apple ID. Go to the Purchased tab (on iPad) or Updates > Purchased (on iPhone), scroll to find the desired app, and tap the Download button. The App Store will remember that you've already downloaded the app, and will offer you an older version of the app compatible with your older device.

Note: You can't skip step #1. If you look for the app directly from your older iOS device, without having first downloaded it to your Mac or PC, the App Store won't show it to you.